Final answer:
The algebraic expression for 'eight decreased by three times the sum of a number and six' is written as 8 - 3(x + 6).
Step-by-step explanation:
The algebraic expression for 'eight decreased by three times the sum of a number and six' would be represented by:
8 - 3(x + 6).
To break this down: 'eight decreased' points to the number 8 starting the expression. The word 'by' signals subtraction. 'Three times' suggests multiplication by 3. 'The sum of a number and six' would be translated as (x + 6), where x is the variable representing the number in question. Therefore, we have three times the sum which is 3(x + 6), and eight decreased by this quantity, giving us the complete expression 8 - 3(x + 6).